The Hepatitis C virus can be transmitted parenteraly, which means that the virus has to reach your blood circulation in order to infect you. Ways of transmitting the disease are: using the same needle as an infected drug-abuser; blood transfusions; unprotected sex; from mother to fetus, and contact to infected blood through damaged skin. In the case of injuries, this means that the skin has to be injured by a wound and the wound must come in contact with someone’s infected blood.
In your case, it depends if the person who bit you was positive for hepatitis C at the moment of contact and if you touched blood with an open wound.